Would an AI with human intelligence have the same rights as a human under current legal frameworks?
Yes, to some of what you propose.  No to some.

Today corporations are granted rights: to own property, earn income, pay taxes, contribute to political campaigns, offer opinion in public, ad more.  Even now I see no reason why an AI should not be eligible to incorporate itself, thereby inheriting all these rights.  Conversely, any corporation already in existence could become fully automated at any time (and some plausibly will).  In doing so, they should not lose any of the rights and duties they currently employ.

However I suspect certain rights would be unavailable to an AI just as they are unavailable to a corporation now: marriage, draft or voluntary service in the military, rights due a parent or child or spouse, estate inheritance, etc.

Could this schizoid sense of human identity be resolved at some point?  Sure.  Already there have been numerous laws introduced and some passed elevating various nonhuman species to higher levels of civil rights that only humans heretofore enjoyed: chimpanzees, cetaceans, parrots and others have been identified as 'higher functioning' and longer lived, and so, are now protected from abuse in ways that food animals, pets, and lab animals are not.  

Once AI 'beings' arise that operate for years and express intelligence and emotions that approach human-level and lifetime, I would expect a political will to arise to define, establish, and defend their civil rights.  And as humans become more cybernetically augmented, especially cognitively, the line that separates us from creatures of pure silicon will begin to blur.  In time it will become unconscionable to overlook the rights of beings simply because they contain 'too little flesh'.